Problem: Simplify; express your answer in exponential form. Assume $a\neq 0, y\neq 0$. $\dfrac{{(a^{-3})^{-2}}}{{a^{5}y^{5}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${a^{-3}}$ to the exponent ${-2}$ . Now ${-3 \times -2 = 6}$ , so ${(a^{-3})^{-2} = a^{6}}$ In the denominator, we can use the distributive property of exponents. ${a^{5}y^{5} = a^{5}y^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(a^{-3})^{-2}}}{{a^{5}y^{5}}} = \dfrac{{a^{6}}}{{a^{5}y^{5}}}$ Break up the equation by variable and simplify. $\dfrac{{a^{6}}}{{a^{5}y^{5}}} = \dfrac{{a^{6}}}{{a^{5}}} \cdot \dfrac{{1}}{{y^{5}}} = a^{{6} - {5}} \cdot y^{- {5}} = ay^{-5}$.